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n_sinh.c revision 1.2 
      1 /*      $NetBSD: n_sinh.c,v 1.2 1997/10/20 14:13:27 ragge Exp $ */
      2 /*
      3  * Copyright (c) 1985, 1993
      4  *	The Regents of the University of California.  All rights reserved.
      5  *
      6  * Redistribution and use in source and binary forms, with or without
      7  * modification, are permitted provided that the following conditions
      8  * are met:
      9  * 1. Redistributions of source code must retain the above copyright
     10  *    notice, this list of conditions and the following disclaimer.
     11  * 2. Redistributions in binary form must reproduce the above copyright
     12  *    notice, this list of conditions and the following disclaimer in the
     13  *    documentation and/or other materials provided with the distribution.
     14  * 3. All advertising materials mentioning features or use of this software
     15  *    must display the following acknowledgement:
     16  *	This product includes software developed by the University of
     17  *	California, Berkeley and its contributors.
     18  * 4. Neither the name of the University nor the names of its contributors
     19  *    may be used to endorse or promote products derived from this software
     20  *    without specific prior written permission.
     21  *
     22  * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
     23  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
     24  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
     25  * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
     26  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
     27  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
     28  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
     29  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
     30  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
     31  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
     32  * SUCH DAMAGE.
     33  */
     34 
     35 #ifndef lint
     36 #if 0
     37 static char sccsid[] = "@(#)sinh.c	8.1 (Berkeley) 6/4/93";
     38 #endif
     39 #endif /* not lint */
     40 
     41 /* SINH(X)
     42  * RETURN THE HYPERBOLIC SINE OF X
     43  * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
     44  * CODED IN C BY K.C. NG, 1/8/85;
     45  * REVISED BY K.C. NG on 2/8/85, 3/7/85, 3/24/85, 4/16/85.
     46  *
     47  * Required system supported functions :
     48  *	copysign(x,y)
     49  *	scalb(x,N)
     50  *
     51  * Required kernel functions:
     52  *	expm1(x)	...return exp(x)-1
     53  *
     54  * Method :
     55  *	1. reduce x to non-negative by sinh(-x) = - sinh(x).
     56  *	2.
     57  *
     58  *	                                      expm1(x) + expm1(x)/(expm1(x)+1)
     59  *	    0 <= x <= lnovfl     : sinh(x) := --------------------------------
     60  *			       		                      2
     61  *     lnovfl <= x <= lnovfl+ln2 : sinh(x) := expm1(x)/2 (avoid overflow)
     62  * lnovfl+ln2 <  x <  INF        :  overflow to INF
     63  *
     64  *
     65  * Special cases:
     66  *	sinh(x) is x if x is +INF, -INF, or NaN.
     67  *	only sinh(0)=0 is exact for finite argument.
     68  *
     69  * Accuracy:
     70  *	sinh(x) returns the exact hyperbolic sine of x nearly rounded. In
     71  *	a test run with 1,024,000 random arguments on a VAX, the maximum
     72  *	observed error was 1.93 ulps (units in the last place).
     73  *
     74  * Constants:
     75  * The hexadecimal values are the intended ones for the following constants.
     76  * The decimal values may be used, provided that the compiler will convert
     77  * from decimal to binary accurately enough to produce the hexadecimal values
     78  * shown.
     79  */
     80 
     81 #include "mathimpl.h"
     82 
     83 vc(mln2hi, 8.8029691931113054792E1   ,0f33,43b0,2bdb,c7e2,   7, .B00F33C7E22BDB)
     84 vc(mln2lo,-4.9650192275318476525E-16 ,1b60,a70f,582a,279e, -50,-.8F1B60279E582A)
     85 vc(lnovfl, 8.8029691931113053016E1   ,0f33,43b0,2bda,c7e2,   7, .B00F33C7E22BDA)
     86 
     87 ic(mln2hi, 7.0978271289338397310E2,    10, 1.62E42FEFA39EF)
     88 ic(mln2lo, 2.3747039373786107478E-14, -45, 1.ABC9E3B39803F)
     89 ic(lnovfl, 7.0978271289338397310E2,     9, 1.62E42FEFA39EF)
     90 
     91 #ifdef vccast
     92 #define	mln2hi	vccast(mln2hi)
     93 #define	mln2lo	vccast(mln2lo)
     94 #define	lnovfl	vccast(lnovfl)
     95 #endif
     96 
     97 #if defined(vax)||defined(tahoe)
     98 static max = 126                      ;
     99 #else	/* defined(vax)||defined(tahoe) */
    100 static max = 1023                     ;
    101 #endif	/* defined(vax)||defined(tahoe) */
    102 
    103 
    104 double sinh(x)
    105 double x;
    106 {
    107 	static const double  one=1.0, half=1.0/2.0 ;
    108 	double t, sign;
    109 #if !defined(vax)&&!defined(tahoe)
    110 	if(x!=x) return(x);	/* x is NaN */
    111 #endif	/* !defined(vax)&&!defined(tahoe) */
    112 	sign=copysign(one,x);
    113 	x=copysign(x,one);
    114 	if(x<lnovfl)
    115 	    {t=expm1(x); return(copysign((t+t/(one+t))*half,sign));}
    116 
    117 	else if(x <= lnovfl+0.7)
    118 		/* subtract x by ln(2^(max+1)) and return 2^max*exp(x)
    119 	    		to avoid unnecessary overflow */
    120 	    return(copysign(scalb(one+expm1((x-mln2hi)-mln2lo),max),sign));
    121 
    122 	else  /* sinh(+-INF) = +-INF, sinh(+-big no.) overflow to +-INF */
    123 	    return( expm1(x)*sign );
    124 }
    125